Calculating Final Angular Velocity of Turntable with Runner on a Horizontal Axis

[reminiscent]

Homework Statement

A 55 kg runner runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the Earth has magnitude of 3.1 m/s. The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.20 rad/s relative to the earth. The radius of the turntable is 3.0 m, and its moment of inertia about the axis of rotation is 120 kg-m2. Find the final angular velocity of the turntable if the runner slows to a walk in such a way that she is at rest relative to the earth.

Homework Equations

ΔL = 0
L1 = L2

The Attempt at a Solution

This was ripped off from a problem in the book that asked for "the final angular velocity of the system if the runner comes to rest relative to the turntable," which I did just that, but I just noticed that this problem's last sentence is a different variation (final angular velocity of the turntable if the runner slows to a walk in such a way that she is at rest relative to the earth.")
Here is what I did - should I change anything at the end?

 

[haruspex]

Your working is not easy to read (posting images is for diagrams and printed/typed matter) and you do not define your variables, which makes it hard to follow.
I get a different answer.

 

[reminiscent]

Your working is not easy to read (posting images is for diagrams and printed/typed matter) and you do not define your variables, which makes it hard to follow.
I get a different answer.

Well T stands for turntable and R stands for runner. L1 was the initial and L2 was the final. L1 consisted of the angular momentums of both the turntable and runner. I treated them as a system at the end having the same angular velocity.

 

[reminiscent]

Can anyone tell me what I did wrong?

 

[reminiscent]

Your working is not easy to read (posting images is for diagrams and printed/typed matter) and you do not define your variables, which makes it hard to follow.
I get a different answer.

I got a new answer of -4.06 rad/s.

 

[haruspex]

I got a new answer of -4.06 rad/s.

That's right.